JLMr. B,
There is discussion of this topic on here, but it's generally mixed deeply in with other stuff.
I don't know what country your friend will be moving to, so some issues I may not know about. In most cases the issue arises from the Chinese side. China does not recognize dual citizenships, so Chinese who take citizenship in another country are required by the Chinese government to give up their Chinese citizen status.
Most countries require residency for two years or more before they grant citizenship, so your friend shouldn't have a problem at first...she'll still be a Chinese national and able to at least re-enter China freely. (She'll still need the proper Chinese passport and foreign visa in order to leave again...)
Once she's a citizen of her new home, though, she'll be viewed by the Chinese Consulates just like any other national of her husband's country. She'll need to obtain and maintain the correct Chinese visa in order to cross the border or stay in China, just as we must. For many countries, this is no problem...citizens of the USA, Canada, Australia, New Zealand, most Western European countries, and many others can get a Chinese visa quite easily.
Can Chinese people hide a second citizenship? Sure, and a fair number of them do. There are some risks, but it can be and is done.
Problems? Probably not. If she's going to South or Southeast Asia, maybe.
Or if she wants to come back to visit for an extended time, for example to care for an ailing parent, it's possible that she'd have a hard time keeping a visa. Of course, she'd probably lose all access to any Chinese social benefits she may have had. There are also some individual variables...some police and bureaucrats tend to harass Chinese women who marry foreigners. But none of these seem terribly likely or terribly worrisome.
All in all, from what I know of the situation she doesn't seem to really have too much to worry about.